## Height of Tetrahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Height of Tetrahedron = sqrt((2*Total Surface Area of Tetrahedron)/(3*sqrt(3)))
h = sqrt((2*TSA)/(3*sqrt(3)))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Height of Tetrahedron - (Measured in Meter) - Height of Tetrahedron is the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex.
Total Surface Area of Tetrahedron - (Measured in Square Meter) - Total Surface Area of Tetrahedron is the total quantity of plane enclosed by the entire surface of the Tetrahedron.
STEP 1: Convert Input(s) to Base Unit
Total Surface Area of Tetrahedron: 170 Square Meter --> 170 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h = sqrt((2*TSA)/(3*sqrt(3))) --> sqrt((2*170)/(3*sqrt(3)))
Evaluating ... ...
h = 8.08906858100224
STEP 3: Convert Result to Output's Unit
8.08906858100224 Meter --> No Conversion Required
FINAL ANSWER
8.08906858100224 8.089069 Meter <-- Height of Tetrahedron
(Calculation completed in 00.003 seconds)
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## Credits

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 8 Height of Tetrahedron Calculators

Height of Tetrahedron given Total Surface Area
Height of Tetrahedron = sqrt((2*Total Surface Area of Tetrahedron)/(3*sqrt(3)))
Height of Tetrahedron given Volume
Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)
Height of Tetrahedron given Face Area
Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))
Height of Tetrahedron given Midsphere Radius
Height of Tetrahedron = 2*sqrt(4/3)*Midsphere Radius of Tetrahedron
Height of Tetrahedron
Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron
Height of Tetrahedron given Surface to Volume Ratio
Height of Tetrahedron = 12/Surface to Volume Ratio of Tetrahedron
Height of Tetrahedron given Circumsphere Radius
Height of Tetrahedron = 4/3*Circumsphere Radius of Tetrahedron
Height of Tetrahedron given Insphere Radius
Height of Tetrahedron = 4*Insphere Radius of Tetrahedron

## Height of Tetrahedron given Total Surface Area Formula

Height of Tetrahedron = sqrt((2*Total Surface Area of Tetrahedron)/(3*sqrt(3)))
h = sqrt((2*TSA)/(3*sqrt(3)))

## What is a Tetrahedron?

A Tetrahedron is a symmetric and closed three dimensional shape with 4 identical equilateral triangular faces. It is a Platonic solid, which has 4 faces, 4 vertices and 6 edges. At each vertex, three equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

## What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

## How to Calculate Height of Tetrahedron given Total Surface Area?

Height of Tetrahedron given Total Surface Area calculator uses Height of Tetrahedron = sqrt((2*Total Surface Area of Tetrahedron)/(3*sqrt(3))) to calculate the Height of Tetrahedron, The Height of Tetrahedron given Total Surface Area formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the total surface area of the Tetrahedron. Height of Tetrahedron is denoted by h symbol.

How to calculate Height of Tetrahedron given Total Surface Area using this online calculator? To use this online calculator for Height of Tetrahedron given Total Surface Area, enter Total Surface Area of Tetrahedron (TSA) and hit the calculate button. Here is how the Height of Tetrahedron given Total Surface Area calculation can be explained with given input values -> 8.089069 = sqrt((2*170)/(3*sqrt(3))).

### FAQ

What is Height of Tetrahedron given Total Surface Area?
The Height of Tetrahedron given Total Surface Area formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the total surface area of the Tetrahedron and is represented as h = sqrt((2*TSA)/(3*sqrt(3))) or Height of Tetrahedron = sqrt((2*Total Surface Area of Tetrahedron)/(3*sqrt(3))). Total Surface Area of Tetrahedron is the total quantity of plane enclosed by the entire surface of the Tetrahedron.
How to calculate Height of Tetrahedron given Total Surface Area?
The Height of Tetrahedron given Total Surface Area formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the total surface area of the Tetrahedron is calculated using Height of Tetrahedron = sqrt((2*Total Surface Area of Tetrahedron)/(3*sqrt(3))). To calculate Height of Tetrahedron given Total Surface Area, you need Total Surface Area of Tetrahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area of Tetrahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Height of Tetrahedron?
In this formula, Height of Tetrahedron uses Total Surface Area of Tetrahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -
• Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron
• Height of Tetrahedron = 4/3*Circumsphere Radius of Tetrahedron
• Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))
• Height of Tetrahedron = 4*Insphere Radius of Tetrahedron
• Height of Tetrahedron = 2*sqrt(4/3)*Midsphere Radius of Tetrahedron
• Height of Tetrahedron = 12/Surface to Volume Ratio of Tetrahedron
• Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)
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